Rotational Symmetry Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Equilateral triangle ABCABC is centred at the origin. A 120°120° counterclockwise rotation maps A→BA \to B. What does CC map to, and what is the order of symmetry?

Solution

  1. 1
    A 120°120° CCW rotation cycles all three vertices: A→BA \to B, B→CB \to C, C→AC \to A.
  2. 2
    So vertex CC maps to vertex AA.
  3. 3
    The triangle maps to itself after 120°120°, 240°240°, and 360°360°. The order of symmetry is 33.

Answer

CC maps to AA; the equilateral triangle has rotational symmetry of order 33.
An equilateral triangle is invariant under rotations of 120°120° and 240°240°. Each rotation permutes the vertices cyclically, and after three rotations the triangle returns to its original orientation.

About Rotational Symmetry

A figure has rotational symmetry if it looks identical after being rotated by some angle less than 360°360° about a central point. The order of rotational symmetry is the number of distinct positions where the figure looks the same during a full rotation.

Learn more about Rotational Symmetry →

More Rotational Symmetry Examples

Example 1 easy

Determine the order of rotational symmetry and the minimum angle of rotation for a regular hexagon.

Example 2 medium

Which of the letters 'S' and 'H' has rotational symmetry? State the order and angle for each that qu

Example 3 easy

A figure has rotational symmetry of order [formula]. List all angles of rotation that map it onto it

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